Find the Equation Using Two Points (0,2) , (4,5)

$(0, 2)$ , $(4, 5)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

Step 3

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{5 - (2)}{4 - (0)}$

Step 5

Finding the slope $m$ .

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{5 - 2}{4 - (0)}$

Subtract $2$ from $5$ .

$m = \frac{3}{4 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{3}{4 + 0}$

Add $4$ and $0$ .

$m = \frac{3}{4}$

Step 6

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (\frac{3}{4}) x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{3}{4}) \cdot (0) + b$

Substitute the value of $y$ into the equation.

$2 = (\frac{3}{4}) \cdot (0) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{3}{4} \cdot 0 + b = 2$ .

$\frac{3}{4} \cdot 0 + b = 2$

Simplify $\frac{3}{4} \cdot 0 + b$ .

Multiply $\frac{3}{4}$ by $0$ .

$0 + b = 2$

Add $0$ and $b$ .

$b = 2$

Step 7

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = \frac{3}{4} x + 2$

Step 8

Find the Equation Using Two Points (0,2) , (4,5)

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